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- Young
childrens
arithmetic
strategies in
social
context: How
parents
contribute to
childrens
strategy
development
while playing
games: International
Journal of
Behavioral
Development,
Vol. 28, No.
4. (July
2004), pp.
347-357. We
examined the
relationship
between
parents'
behaviour and
children's use
of simple
arithmetic
strategies
while playing
a board game
in contrast to
solving
arithmetic
problems. In a
microgenetic
study spanning
3 weeks,
5-year-old
children who
were just
beginning
kindergarten
played a
modified game
of "Chutes and
Ladders" with
one of their
parents,
computing
their moves
from the throw
of dice.
Children also
solved math
problems (math
context) given
to them by
their parents
at the end of
each session.
Children's
arithmetic
strategies and
a variety of
parental
behaviours
(prompt,
prompt after
error,
affirmation,
disaffirmation
, cognitive
directives,
provide
answer) were
coded for
children's
game moves and
the math
context. As in
past research,
children used
multiple and
variable
strategies,
both when
computing
their moves
during the
game and in
solving the
math problems.
Parents
displayed
different
patterns of
behaviours
during the
game and math
contexts and
showed
different
relationships
among
behaviours and
strategies as
a function of
context,
reflecting
their
sensitivity to
the cognitive
demands on
their children
of the
different
tasks. The
results were
interpreted in
terms of the
need to
integrate
contemporary
strategy
development
theory with a
sociocultural
perspective
and to
recognise the
dynamic nature
of
parent-child
interactions
with respect
to the social
construction
of cognitive
strategies.
Source: International Journal of Behavioral Development, Vol. 28, No. 4. (July 2004), pp. 347-357. - Transforming
society by
transforming
technology:
the science
and politics
of
participatory
design: Accounting,
Management and
Information
Technologies,
Vol. 10, No.
4. (October
2000), pp.
257-290.
Source: Accounting, Management and Information Technologies, Vol. 10, No. 4. (October 2000), pp. 257-290. - Incompressible
Euler
Equations: the
blow-up
problem and
related
results: (14 Mar
2007)The
question of
spontaneous
apparition of
singularity in
the 3D
incompressible
Euler
equations is
one of the
most important
and
challenging
open problems
in
mathematical
fluid
mechanics. In
this survey
article we
review some of
recent
approaches to
the problem.
We first
review Kato's
classical
local
well-posedness
result in the
Sobolev space
and derive the
celebrated
Beale-Kato-Maj
da criterion
for finite
time blow-up.
Then, we
discuss recent
refinements of
the criterion
as well as
geometric type
of theorems on
the
sufficiency
condition for
the regularity
of solutions.
After that we
review results
excluding some
of the
scenarios
leading to
finite time
singularities.
We also survey
studies of
various
simplified
model
problems. A
dichotomy type
of result
between the
finite time
blow-up and
the global in
time regular
dynamics is
presented, and
a spectral
dynamics
approach to
study local in
time behaviors
of the
enstrophy is
also reviewed.
Finally,
progresses on
the problem of
optimal
regularity for
solutions to
have conserved
quantities are
presented.
Source: (14 Mar 2007) - Thermodynamic
formalism and
large
deviation
functions in
continuous
time Markov
dynamics: (16 Mar
2007)The
thermodynamic
formalism,
which was
first
developed for
dynamical
systems and
then applied
to discrete
Markov
processes,
turns out to
be well suited
for continuous
time Markov
processes as
well, provided
the
definitions
are
interpreted in
an appropriate
way. Besides,
it can be
reformulated
in terms of
the generating
function of an
observable,
and then
extended to
other
observables.
In particular,
the simple
observable $K$
giving the
number of
events
occurring over
a given time
interval turns
out to contain
already the
signature of
dynamical
phase
transitions.
For mean-field
models in
equilibrium,
and in the
limit of large
systems, the
formalism is
rather simple
to apply and
shows how
thermodynamic
phase
transitions
may modify the
dynamical
properties of
the systems.
This is
exemplified
with the
q-state
mean-field
Potts model,
for which the
Ising limit
q=2 is found
to be
qualitatively
different from
the other
cases.
Source: (16 Mar 2007) - Euler
Equations of
Incompressible
Ideal Fluids: (14 Mar
2007)This
article is a
survey
concerning the
state-of-the-a
rt
mathematical
theory of the
Euler
equations of
incompressible
homogenous
ideal fluid.
Emphasis is
put on the
different
types of
emerging
instability,
and how they
may be related
to the
description of
turbulence.
Source: (14 Mar 2007) - A Geometric
Mechanism For
Diffusion In: We introduce a
geometric
mechanism for
di#usion in a
priori
unstable
nearly
integrable
dynamical
systems. It is
based on the
observation
that
resonances,
besides
destroying the
primary KAM
tori, create
secondary tori
and tori of
lower
dimension. We
argue that
these objects
created by
resonances can
be
incorporated
in transition
chains taking
the place of
the destroyed
primary KAM
tori.
- Ergodic
decomposition
of
quasi-invarian
t probability
measures: Colloq. Math.,
Vol. 84/85,
No. , part 2.
(2000), pp.
495-514.
Source: Colloq. Math., Vol. 84/85, No. , part 2. (2000), pp. 495-514. - Classes of
small-world
networks.: Proc Natl Acad
Sci U S A,
Vol. 97, No.
21. (10
October 2000),
pp.
11149-11152.We
study the
statistical
properties of
a variety of
diverse
real-world
networks. We
present
evidence of
the occurrence
of three
classes of
small-world
networks: (a)
scale-free
networks,
characterized
by a vertex
connectivity
distribution
that decays as
a power law;
(b)
broad-scale
networks,
characterized
by a
connectivity
distribution
that has a
power law
regime
followed by a
sharp cutoff;
and (c)
single-scale
networks,
characterized
by a
connectivity
distribution
with a fast
decaying tail.
Moreover, we
note for the
classes of
broad-scale
and
single-scale
networks that
there are
constraints
limiting the
addition of
new links. Our
results
suggest that
the nature of
such
constraints
may be the
controlling
factor for the
emergence of
different
classes of
networks.
Source: Proc Natl Acad Sci U S A, Vol. 97, No. 21. (10 October 2000), pp. 11149-11152. - Estimates on
Invariant Tori
Near an
Elliptic
Equilibrium
Point of a
Hamiltonian
System: (1996)We give
a precise
statement for
KAM theorem in
a
neighbourhood
of an elliptic
equilibrium
point of a
Hamiltonian
system. If the
frequencies of
the elliptic
point are
nonresonant up
to a certain
order K 4, and
a
nondegeneracy
condition is
fulfilled, we
get an
estimate for
the measure of
the complement
of the KAM
tori in a
neighbourhood
of given
radius.
Moreover, if
the
frequencies
satisfy a
Diophantine
condition,
with exponent
ø , we show
that in a
neighbourhood
of radius r
the measure of
the...
Source: (1996) - Nonergodic
actions,
cocycles and
superrigidity: New York J.
Math., Vol. 10
(2004), pp.
249-269
(electronic).
Source: New York J. Math., Vol. 10 (2004), pp. 249-269 (electronic).
If you would like to find additional social bookmark based links on the topic of math we recommend the Open Tag Directory > Math. If you would like to find related tags we recommend Tag Patterns > Math.
